Atkin-Lehner |
2- 3- 89+ |
Signs for the Atkin-Lehner involutions |
Class |
51264bd |
Isogeny class |
Conductor |
51264 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
43008 |
Modular degree for the optimal curve |
Δ |
-3189030912 = -1 · 214 · 37 · 89 |
Discriminant |
Eigenvalues |
2- 3- 4 2 -2 -2 -8 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-48,-2720] |
[a1,a2,a3,a4,a6] |
Generators |
[130:225:8] |
Generators of the group modulo torsion |
j |
-1024/267 |
j-invariant |
L |
8.3224426731615 |
L(r)(E,1)/r! |
Ω |
0.63371630856498 |
Real period |
R |
3.2831894021993 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000043 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
51264o1 12816c1 17088n1 |
Quadratic twists by: -4 8 -3 |